joint work with Wim Van Ackooij, Jerome Malick, Wellington De Oliveira, Guilherme Ramalho
Probabilistic constraints (or chance constraints) aim at providing safety regions for optimization problems exposed to uncertainty. Understanding when these regions are convex is important for numerical resolution of the optimization problem. In this work we show that “eventual convexity” often occurs : for structured but general models of chance constraints, convexity of levels sets is guaranteed when the probability level is greater than a computable threshold. We illustrate our results on examples uncovered by previous theory.
joint work with René Henrion, Wim Van Ackooij
Ideas from robust optimization lead to probust functions, i.e. probability functions acting on generalized semi-infinite inequality systems. In this work, we employ powerful tools from variational analysis to study generalized differentiation of such probust functions. We also provide explicit outer estimates of the generalized subdifferentials in terms of nominal data.